Global Riemannian Geometry: Curvature and Topology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser Basel
2003
|
| Series: | Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemàtica
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| Subjects: | |
| Online Access: | Volltext |
| Item Description: | In July 2001, the Centre de Recerca Matematica organised at the Universitat Jaume I, in Castello de la Plana, a 20 hour Advanced Course on global Riemannian geometry: curvature and topology. We focused our talks on two main topics: a) The comparison theory for distance functions in spaces which have well defined bounds on their curvature. In this setting we obtained information about diffusion processes, isoperimetric inequalities, transience, and effective resistance of the spaces in question. b) The study of Gromov's invariants to measure the K-theoretic size of a Rie mannian manifold by using the famous Lichnerowicz formula for Dirac operators. After the course was finished we extended and smoothed out the material presented in the lectures, and integrated it with the background material furnished to the participants and with their many interesting comments. It is our great pleasure to thank Professor Vicent Palmer, the local organisers Ximo Gual, Ana Lluch and Vicent Miquel, the Centre de Recerca Matematica (CRM) and the Universitat Jaume I for the invitation, the cordial hospitality, the favourable planning of the course and the stimulating working atmosphere. Contents Distance Geometric Analysis on Manifolds Steen Markvorsen 1 Appetizer and Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 The Comparison Setting and Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Analysis of Restricted Distance Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 Concerning the Setting and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 Green's Formulae and the Co-area Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6 The First Dirichlet Eigenvalue Comparison Theorem . . . . . . . . . . . . . . . . . . . . . 13 7 Isoperimetric Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 7. 1 Preliminary Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
| Physical Description: | 1 Online-Ressource (100p) |
| ISBN: | 9783034880558 9783764321703 |
| DOI: | 10.1007/978-3-0348-8055-8 |
Staff View
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| 500 | |a In July 2001, the Centre de Recerca Matematica organised at the Universitat Jaume I, in Castello de la Plana, a 20 hour Advanced Course on global Riemannian geometry: curvature and topology. We focused our talks on two main topics: a) The comparison theory for distance functions in spaces which have well defined bounds on their curvature. In this setting we obtained information about diffusion processes, isoperimetric inequalities, transience, and effective resistance of the spaces in question. b) The study of Gromov's invariants to measure the K-theoretic size of a Rie mannian manifold by using the famous Lichnerowicz formula for Dirac operators. After the course was finished we extended and smoothed out the material presented in the lectures, and integrated it with the background material furnished to the participants and with their many interesting comments. | ||
| 500 | |a It is our great pleasure to thank Professor Vicent Palmer, the local organisers Ximo Gual, Ana Lluch and Vicent Miquel, the Centre de Recerca Matematica (CRM) and the Universitat Jaume I for the invitation, the cordial hospitality, the favourable planning of the course and the stimulating working atmosphere. Contents Distance Geometric Analysis on Manifolds Steen Markvorsen 1 Appetizer and Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 The Comparison Setting and Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Analysis of Restricted Distance Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 Concerning the Setting and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 Green's Formulae and the Co-area Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | ||
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
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| spelling | Markvorsen, Steen Verfasser aut Global Riemannian Geometry: Curvature and Topology by Steen Markvorsen, Maung Min-Oo Basel Birkhäuser Basel 2003 1 Online-Ressource (100p) txt rdacontent c rdamedia cr rdacarrier Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemàtica In July 2001, the Centre de Recerca Matematica organised at the Universitat Jaume I, in Castello de la Plana, a 20 hour Advanced Course on global Riemannian geometry: curvature and topology. We focused our talks on two main topics: a) The comparison theory for distance functions in spaces which have well defined bounds on their curvature. In this setting we obtained information about diffusion processes, isoperimetric inequalities, transience, and effective resistance of the spaces in question. b) The study of Gromov's invariants to measure the K-theoretic size of a Rie mannian manifold by using the famous Lichnerowicz formula for Dirac operators. After the course was finished we extended and smoothed out the material presented in the lectures, and integrated it with the background material furnished to the participants and with their many interesting comments. It is our great pleasure to thank Professor Vicent Palmer, the local organisers Ximo Gual, Ana Lluch and Vicent Miquel, the Centre de Recerca Matematica (CRM) and the Universitat Jaume I for the invitation, the cordial hospitality, the favourable planning of the course and the stimulating working atmosphere. Contents Distance Geometric Analysis on Manifolds Steen Markvorsen 1 Appetizer and Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 The Comparison Setting and Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 3 Analysis of Restricted Distance Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 4 Concerning the Setting and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 Green's Formulae and the Co-area Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 6 The First Dirichlet Eigenvalue Comparison Theorem . . . . . . . . . . . . . . . . . . . . . 13 7 Isoperimetric Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 7. 1 Preliminary Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mathematics Global analysis Global differential geometry Cell aggregation / Mathematics Global Analysis and Analysis on Manifolds Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Globale Riemannsche Geometrie (DE-588)4157622-6 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Riemannscher Raum (DE-588)4128295-4 s 1\p DE-604 Globale Riemannsche Geometrie (DE-588)4157622-6 s 2\p DE-604 Min-Oo, Maung Sonstige oth https://doi.org/10.1007/978-3-0348-8055-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Markvorsen, Steen Global Riemannian Geometry: Curvature and Topology Mathematics Global analysis Global differential geometry Cell aggregation / Mathematics Global Analysis and Analysis on Manifolds Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Globale Riemannsche Geometrie (DE-588)4157622-6 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4157622-6 (DE-588)4128295-4 |
| title | Global Riemannian Geometry: Curvature and Topology |
| title_auth | Global Riemannian Geometry: Curvature and Topology |
| title_exact_search | Global Riemannian Geometry: Curvature and Topology |
| title_full | Global Riemannian Geometry: Curvature and Topology by Steen Markvorsen, Maung Min-Oo |
| title_fullStr | Global Riemannian Geometry: Curvature and Topology by Steen Markvorsen, Maung Min-Oo |
| title_full_unstemmed | Global Riemannian Geometry: Curvature and Topology by Steen Markvorsen, Maung Min-Oo |
| title_short | Global Riemannian Geometry: Curvature and Topology |
| title_sort | global riemannian geometry curvature and topology |
| topic | Mathematics Global analysis Global differential geometry Cell aggregation / Mathematics Global Analysis and Analysis on Manifolds Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgeometrie (DE-588)4012248-7 gnd Globale Riemannsche Geometrie (DE-588)4157622-6 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Mathematics Global analysis Global differential geometry Cell aggregation / Mathematics Global Analysis and Analysis on Manifolds Differential Geometry Manifolds and Cell Complexes (incl. Diff.Topology) Mathematik Differentialgeometrie Globale Riemannsche Geometrie Riemannscher Raum |
| url | https://doi.org/10.1007/978-3-0348-8055-8 |
| work_keys_str_mv | AT markvorsensteen globalriemanniangeometrycurvatureandtopology AT minoomaung globalriemanniangeometrycurvatureandtopology |